Kompfner was born in Vienna to Jewish parents.
[1] He was originally trained as an architect and after receiving his university degree in 1933 he moved to England (due to the rise of anti-Semitism), where he worked as an architect until 1941.
He had a strong interest in physics and electronics, and after being briefly detained by the British at the start of World War II he was recruited to work in a secret microwave vacuum tube research program at the University of Birmingham.
After the war he became a British citizen, continued working for the Admiralty as a scientist, and also studied physics at the University of Oxford, receiving his D.Phil.
[2] In 1965, he received an honorary doctorate from the Vienna University of Technology.